A many-objective evolutionary algorithm based on rotated grid

Abstract Evolutionary optimization algorithms, a meta-heuristic approach, often encounter considerable challenges in many-objective optimization problems (MaOPs). The Pareto-based dominance loses its effectiveness in MaOPs, which are defined as having more than three objectives. Therefore, a more valid selection method is proposed to balance convergence and distribution. This paper proposes an algorithm using rotary grid technology to solve MaOPs (denoted by RGridEA). The algorithm uses the rotating grid to partition the objective space. Instead of using the Pareto non-dominated sorting strategy to layer the population a novel stratified method is used to enhance convergence effectively and make use of the grid to improve distribution and uniformity. Finally, with the other seven algorithm was tested on the test function DTLZ series analysis, confirming RGridEA is effective in resolving MaOPs.

[1]  M. Farina,et al.  On the optimal solution definition for many-criteria optimization problems , 2002, 2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622).

[2]  Shengxiang Yang,et al.  A Grid-Based Evolutionary Algorithm for Many-Objective Optimization , 2013, IEEE Transactions on Evolutionary Computation.

[3]  Evan J. Hughes,et al.  Radar Waveform Optimisation as a Many-Objective Application Benchmark , 2007, EMO.

[4]  Carlos A. Coello Coello,et al.  Preference incorporation to solve many-objective airfoil design problems , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[5]  Shengxiang Yang,et al.  The effect of diversity maintenance on prediction in dynamic multi-objective optimization , 2017, Appl. Soft Comput..

[6]  Sanaz Mostaghim,et al.  Distance Based Ranking in Many-Objective Particle Swarm Optimization , 2008, PPSN.

[7]  Ming Yang,et al.  A New Evolutionary Decision Theory for Many-Objective Optimization Problems , 2007, ISICA.

[8]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[9]  Kalyanmoy Deb,et al.  Running performance metrics for evolutionary multi-objective optimizations , 2002 .

[10]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[11]  A. Tamhane.  Multiple comparisons in model i one-way anova with unequal variances , 1977 .

[12]  Prabhat Hajela,et al.  Genetic search strategies in multicriterion optimal design , 1991 .

[13]  J. Bader.  An algorithm for fast hypervolume-based many-objective optimization , 2008 .

[14]  Rolf Drechsler,et al.  Robust Multi-Objective Optimization in High Dimensional Spaces , 2007, EMO.

[15]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

[16]  Rolf Drechsler,et al.  Multi-objective Optimisation Based on Relation Favour , 2001, EMO.

[17]  Evan J. Hughes,et al.  Evolutionary many-objective optimisation: many once or one many? , 2005, 2005 IEEE Congress on Evolutionary Computation.

[18]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[19]  Dirk Thierens,et al.  The balance between proximity and diversity in multiobjective evolutionary algorithms , 2003, IEEE Trans. Evol. Comput..

[20]  Lucas Bradstreet,et al.  A Fast Incremental Hypervolume Algorithm , 2008, IEEE Transactions on Evolutionary Computation.

[21]  Qingfu Zhang,et al.  Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms , 2013, IEEE Transactions on Evolutionary Computation.

[22]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[23]  R. Lakshmi,et al.  A New Biological Operator in Genetic Algorithm for Class Scheduling Problem , 2012 .

[24]  H. Kita,et al.  Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[25]  Nicola Beume,et al.  Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization , 2007, EMO.

[26]  Shengxiang Yang,et al.  Diversity Comparison of Pareto Front Approximations in Many-Objective Optimization , 2014, IEEE Transactions on Cybernetics.

[27]  David W. Corne,et al.  Quantifying the Effects of Objective Space Dimension in Evolutionary Multiobjective Optimization , 2007, EMO.

[28]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[29]  Peter J. Fleming,et al.  Preference-Driven Co-evolutionary Algorithms Show Promise for Many-Objective Optimisation , 2011, EMO.

[30]  Evan J. Hughes.  Fitness Assignment Methods for Many-Objective Problems , 2008, Multiobjective Problem Solving from Nature.

[31]  Kalyanmoy Deb,et al.  Non-linear Dimensionality Reduction Procedures for Certain Large-Dimensional Multi-objective Optimization Problems: Employing Correntropy and a Novel Maximum Variance Unfolding , 2007, EMO.

[32]  David W. Corne,et al.  Techniques for highly multiobjective optimisation: some nondominated points are better than others , 2007, GECCO '07.

[33]  Eckart Zitzler,et al.  Improving hypervolume-based multiobjective evolutionary algorithms by using objective reduction methods , 2007, 2007 IEEE Congress on Evolutionary Computation.

[34]  Soon-Thiam Khu,et al.  An Investigation on Preference Order Ranking Scheme for Multiobjective Evolutionary Optimization , 2007, IEEE Transactions on Evolutionary Computation.

[35]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[36]  Shengxiang Yang,et al.  A prediction strategy based on center points and knee points for evolutionary dynamic multi-objective optimization , 2017, Appl. Soft Comput..

[37]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[38]  Francesco di Pierro,et al.  Many-objective evolutionary algorithms and applications to water resources engineering , 2006 .

[39]  Patrick M. Reed,et al.  Save now, pay later? Multi-period many-objective groundwater monitoring design given systematic model errors and uncertainty , 2011 .

[40]  Shengxiang Yang,et al.  Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization , 2014, IEEE Transactions on Evolutionary Computation.

[41]  E. Hughes.  Multiple single objective Pareto sampling , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[42]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[43]  José M. Molina López,et al.  Effective Evolutionary Algorithms for Many-Specifications Attainment: Application to Air Traffic Control Tracking Filters , 2009, IEEE Transactions on Evolutionary Computation.

[44]  Peter J. Fleming,et al.  A Diversity Management Operator for Evolutionary Many-Objective Optimisation , 2009, EMO.

[45]  Patrick M. Reed,et al.  Diagnostic Assessment of Search Controls and Failure Modes in Many-Objective Evolutionary Optimization , 2012, Evolutionary Computation.

[46]  Peter J. Fleming,et al.  Diversity Management in Evolutionary Many-Objective Optimization , 2011, IEEE Transactions on Evolutionary Computation.

[47]  Eckart Zitzler,et al.  HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization , 2011, Evolutionary Computation.

[48]  Kiyoshi Tanaka,et al.  Self-Controlling Dominance Area of Solutions in Evolutionary Many-Objective Optimization , 2010, SEAL.

[49]  Shengxiang Yang,et al.  A test problem for visual investigation of high-dimensional multi-objective search , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[50]  Carlos A. Coello Coello,et al.  Objective reduction using a feature selection technique , 2008, GECCO '08.

[51]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization: A short review , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).